Question
βAβ is 100% more efficient than βCβ, while
βBβ is 200% more efficient than βAβ. Together, they complete a task in 15 days. After βAβ and βCβ work for 9 days, they stop. How long will βBβ take to finish the remaining work?Solution
Let efficiency of βCβ = x units/day
Efficiency of βAβ = 2x units/day
Efficiency of βBβ = 3 Γ 2x = 6x units/day Total work = (2x + 6x + x) Γ 15
= 9x Γ 15 = 135x units Work done by βAβ and βCβ in 9 days = (2x + x) Γ 9 = 3x Γ 9 = 27x units Remaining work = 135x β 27x = 108x units Time required by βBβ = 108x / 6x = 18 days
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